I hear it's a good idea to drain your gas tank during the months when you store your scoot, but what about other recommended procedures? Should you drain the oil reservoir too? What else do you do when you store your ride?

I recommend FILLING the gas tank, adding Stabil fuel stabilzer and letting the scoot run so that the fuel/mixture gets into the carb. Shut 'er off and park it for the winter. Pulling the battery (if it has one) is a good idea as well--especially if your scooter is being stored in an unheated garage.
You always want to fill a gas tank--PARTICULARLY IF IT'S METAL--as a full tank reduces the possibility of condensation forming in your tank, which reduces the possibilty of rust forming in your tank.
If you have a 4-stroke, change the oil right before you store the bike. Used oil contains acids which will slowly eat away at metal bits over the winter.
-K

I agree with Kevin (oink, oink, flap, flap..... flying pigs) except for the fuel part. I do fill 'er up with stabilized fuel, let it run, but then I turn off the fuel flow and drain the carb. I think this is a good combination of keeping condensation out of a metal fuel tank AND keeping the carbs from getting all gummy.

After some more consideration... Egan's solution makes the most sense.

You don't need to drain your 2-stroke reservior. Stabilize the gas left in your tan (if plastic) and drive it around for a little bit. Then drain the float bowl. Disconnect and bring the battery inside and put on a charger. I reverse my opinion of filling up the tank on a modern scooter after this past spring. that way in the spring you can cut the old gas with some fresh stuff and you have less old stuff to go through. Read all about winter storage in next months issue of Minnesota Motorcycle Monthly on newsstands soon!